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A Course of Modern Analysis

5th Edition


S. J. Patterson
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  • Date Published: August 2021
  • availability: In stock
  • format: Hardback
  • isbn: 9781316518939

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About the Authors
  • This classic work has been a unique resource for thousands of mathematicians, scientists and engineers since its first appearance in 1902. Never out of print, its continuing value lies in its thorough and exhaustive treatment of special functions of mathematical physics and the analysis of differential equations from which they emerge. The book also is of historical value as it was the first book in English to introduce the then modern methods of complex analysis. This fifth edition preserves the style and content of the original, but it has been supplemented with more recent results and references where appropriate. All the formulas have been checked and many corrections made. A complete bibliographical search has been conducted to present the references in modern form for ease of use. A new foreword by Professor S.J. Patterson sketches the circumstances of the book's genesis and explains the reasons for its longevity. A welcome addition to any mathematician's bookshelf, this will allow a whole new generation to experience the beauty contained in this text.

    • The all-time classic textbook, now with references presented in the modern form
    • Never out of print since it first appeared in 1902
    • A unique reference for special functions and the analysis of equations of mathematical physics from which they emerge
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    Reviews & endorsements

    'Generations of mathematicians have referred to W&W, as it has been affectionately called, for information that is difficult to locate elsewhere, in particular, on special functions. This improved new edition will enable future generations to access and learn from one of the great classical texts in the mathematical literature. My personal references to W&W are legion; the cover of my worn copy has long been separated from the text because of constant use.' Bruce C. Berndt, University of Illinois at Urbana-Champaign

    'Many of us who often use special functions revere the classics of complex analysis from the early 20th century. The names of Copson, MacRobert and Titchmarsh come to mind. However, the grandfather, indeed the overarching prototype, for most of these books is the one always referred to as "Whittaker and Watson." Fortunately for the world of mathematics, Victor Moll has presided over this wonderful fifth edition. Victor has provided an exceptionally valuable introduction that provides summaries of each chapter with ties to modern work. This new edition makes it easier for all to use the immense resources therein. Thank you, Victor! Thank you, Cambridge University Press.' George Andrews, The Pennsylvania State University

    'In many cases the coverage here is still the best or one of the best available, and is concise and all in one volume.' Allen Stenger, Mathematical Association of America

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    Product details

    • Edition: 5th Edition
    • Date Published: August 2021
    • format: Hardback
    • isbn: 9781316518939
    • length: 718 pages
    • dimensions: 260 x 185 x 62 mm
    • weight: 1.66kg
    • availability: In stock
  • Table of Contents

    Foreword S. J. Patterson
    Part I. The Process of Analysis:
    1. Complex numbers
    2. The theory of convergence
    3. Continuous functions and uniform convergence
    4. The theory of Riemann integration
    5. The fundamental properties of analytic functions – Taylor's, Laurent's and Liouville's theorems
    6. The theory of residues – application to the evaluation of definite integrals
    7. The expansion of functions in infinite series
    8. Asymptotic expansions and summable series
    9. Fourier series and trigonometric series
    10. Linear differential equations
    11. Integral equations
    Part II. The Transcendental Functions:
    12. The Gamma-function
    13. The zeta-function of Riemann
    14. The hypergeometric function
    15. Legendre functions
    16. The confluent hypergeometric function
    17. Bessel functions
    18. The equations of mathematical physics
    19. Mathieu functions
    20. Elliptic functions. General theorems and the Weierstrassian functions
    21. The theta-functions
    22. The Jacobian elliptic functions
    23. Ellipsoidal harmonics and Lamé's equation
    Appendix. The elementary transcendental functions
    Author index
    Subject index.

  • Authors

    E. T. Whittaker
    E. T. Whittaker was Professor of Mathematics at the University of Edinburgh. He was awarded the Copley Medal in 1954, 'for his distinguished contributions to both pure and applied mathematics and to theoretical physics'.

    G. N. Watson
    G. N. Watson was Professor of Pure Mathematics at the University of Birmingham. He is known, amongst other things, for the 1918 result now known as Watson's lemma and was awarded the De Morgan Medal in 1947.


    Victor H. Moll, Tulane University, Louisiana
    Victor H. Moll is Professor in the Department of Mathematics at Tulane University. He co-authored Elliptic Curves (Cambridge, 1997) and was awarded the Weiss Presidential Award in 2017 for his Graduate Teaching. He first received a copy of Whittaker and Watson during his own undergraduate studies at the Universidad Santa Maria in Chile.


    S. J. Patterson

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